Question

Let 'the coefficient of friction between block B and cart is $\mu (\mu >0)$ and friction is absent everywhere else. Then the values of force F applied to block A such that there is no relative acceleration between block B and cart is :

• A. $\mu mg$
• B. $2\mu mg$
• C. $3\mu mg$
• D. $4\mu mg$

Answer 1

Answer: (A), (B)

The correct options are
A $\mu mg$
B $2\mu mg$

FBD will be as

fs$\to$ static friction.

Then,

let both are moving with acceleration 'a'

$F-fs=ma$ ……..(i)

$fs=ma$ ……..(ii)

$F=2fs$ [From (i) and (ii)]

As $0\le fs\le \mu N\Rightarrow 0\le fs\le \mu mg$

So, $0\le F\le 2\mu mg$

Option (A and B) are correct.